ISTVS embarked on a project in 2016 that aims at updating the current ISTVS standards related to nomenclature, definitions, and measurement techniques for modelling, parameterizing, and, respectively, testing and validation of soft soil parameters and vehicle running gear-terrain interaction. As part of this project, a comprehensive literature review was conducted on the parameterization of fundamental terramechanics models. Soil parameters of the empirical models to assess off-road vehicle mobility, and parameters of the models to characterize the response of the terrain interacting with running gears or plates from the existing terramechanics literature and other researchers' reports were identified. This review documents and summarizes the modelling approaches that may be applicable to real-time applications of terramechanics in simulation, as well as in controller design.